The heat transfer rate will be determined by the material, which is why we like steel woks (for their relatively slow heat transfer and resulting hot spot in the bottom). The heat capacity will be determined by the mass of the wok. The thicker one will heat up slower but stays hot, while the thinner one would heat up and cool down faster. Which is better in that respect? I don't know. Maybe personal preference and how you will use the wok.

Not insignificant, but it may not significant for most users. Like you said, 25% more materials means 25% more heat capacity. So it can store more energy and it also take more time to heat it up...etc..etc. However, it will be approximately 25% in difference, which isn't enough to change people's behavior. Let's think about the time it will take to heat up the woks to the same temperature. For only considering heat absorption without considering heat loss, 25% more mass means 25% more time. So if the 1.6 mm thick wok requires 20 seconds to heat up to a specific temperature, the 2.0 mm thick wok will take 25 second -- 5 second more. If we now include the heat loss process, then the time difference is even smaller.

To me the biggest difference is structure integrity. That is to say, the thick wok will be more sturdy.

I agree with Sid Post. 1.6 mm and 2.0 mm are not huge difference. There will be some differences. Which one is better? It depends on your perspective. The thinner wok will transfer heat faster as you have mention, and will be easily to handle due to its lighter weight. The thicker wok will provide better structural strength and better heat capacity.

Absolutely. I had use a few woks, and the thinner one definitely warp more easily. That being said, I do want to state that warping is not as bad for a carbon steel wok as with other cookware. You can (and I have) hammered a warped wok bottom to flatten it. Flip the wok upside down, place a cloth on the wok bottom, and tap it with a hammer or mallet.

You won't able to do this if it is cast iron wok or if it is a triple cookware.